Wednesday, January 9, 2008

Arbitrage

Earlier I blogged about King Yao's plan to buy Patriots futures and hedge them by betting their opponents to win each individual game.

I was slightly skeptical of the idea at the time, but it looks like Yao is right on. The prevailing odds make New England about a 2-1 favorite to win the AFC, the equivalent of a 66.7% chance.

Based on this week's money lines, the Patriots are about 86.5% to beat Jacksonville. Of those 86.5%, they'll face Indianapolis 68.3% and San Diego 18.2%.

I estimate the oddsmakers will make the Pats 80% favorites over the Colts and 87% favorites over the Chargers. Their net chances of winning the AFC: 70.5%. Indeed, betting the Pats to win the AFC and hedging individual games should show a decent profit.

Maybe my estimate of the Colts-Pats line is off. In that case, you can make a separate bet on Indianapolis to win the AFC, along with New England. The Colts are +375 at 5Dimes, the equivalent of a 21.1% chance to win. Thus, the Colts or Pats need to win the AFC greater than 87.8% of the time for this bet combination to show a profit.

Unlike the Pats future, this bet combination is unaffected by the odds of a potential Colts-Pats game, since you win one bet either way. And even if you assume some totally unrealistic odds for potential AFC Championship matchups (such as NE 80% over SD and Ind 65% over Jax), one of the top two seeds will still win the AFC 90% of the time. With reasonable odds, this number should be over 91%. Either way, proper hedging strategy will guarantee you a small profit.

(By the way, if you'd like to learn to do this kind of analysis on your own, I recommend King Yao's book, Weighing the Odds in Sports Betting. It teaches you most of the necessary skills to make a small profit without any knowledge of sports, and increase your profits if you're a good handicapper.)

The big finish: some updated probability estimates to reflect the latest sportsbook odds: